Shock wave interactions

It is important to note that the state determined by this analysis refers only to the pressure (or normal stress) and particle velocity. The material on either side of the point at which the shock waves collide reach the same pressure-particle velocity state, but other variables may be different from one side to the other. The material on the left-hand side experienced a different loading history than that on the right-hand side. In this example the material on the left-hand side would have a lower final temperature, because the first shock wave was smaller. Such a discontinuity of a variable, other than P or u that arises from a shock wave interaction within a material, is called a contact discontinuity. Contact discontinuities are frequently encountered in the context of inelastic behavior, which will be discussed in Chapter 5. 

The chapters presented by different experts in the field have been structured to develop an intuition for the basic principles by discussing the kinematics of shock compression, first from an extremely fundamental level. These principles include the basic concepts of x-t diagrams, shock-wave interactions, and the continuity equations, which allow the synthesis of material-property data from the measurement of the kinematic properties of shock compression. A good understanding of these principles is prerequisite... 

Shock Relationships and Formulas, which include Changes During Steady Reversible Compressible Flow (61-4) Pressure-Velocity Relationship (65-6) Irreversibility and Degradation (66-8) Derivation of Formulas (68-70) Pressure Efficiency Factor and Recovery Factor (70-2) and Oblique Shocks in Air (72). Shock Wave Interaction, which includes Strong Shock Waves (81) Superposition of Plane Shock Waves (81-2) ... 

Engl transln in Soviet Physics, Doklady 5, 337-40(1960) CA 55, 24013(1961) (Measurement of adiabatic shock waves in cast Trotyl, crystalline Hexogen and Nitromethane) 65) Dunkle s Syllabus (1960-1961) Shock Waves, which includes Mathematical Background (Sessions 1 2) Fluid Flow (Session 3) Initiation of Shock Waves (Session 4) Properties of Shock Waves (Session 5) Shock Relationships and Formulas (Session 6) Shock Wave Interactions (Sessions 7 8) 66) B.D. 

Reynolds number, p 46), etc 61-72 (Shock relationships and formulas) 73-98 (Shock wave interactions formulas) 99-102 (The Rayleigh and Fanno lines) Ibid (1958) 159-6l(Thermal theory of initiation) 168-69 (One-dimensional steady-state process) 169-72 (The Chapman-Jouguet condition) 172-76 (The von Neumann spike) 181-84 (Equations of state and covolume) 184-87 (Polytropic law) 188, 210 212 (Curved front theory of Eyring) 191-94 (The Rayleigh transformation in deton) 210-12 (Nozzle thepry of H. Jones) 285-88 (The deton head model) ... 

Atmospheric effects of large-scale TNT expins have also been studied in depth both practically and theoretically. Factors considered include pressure and impulse effects, decay characteristics and travel and duration times, all as a function of distance, and for both free-field and reflection situations (Refs 3,9,15,16, 17,24,32, 33,34,35,36,44, 53,75,76,115 116). A distinction is made between the blast area dose to the source, comprising air and the products of expln, and that farther away involving air only (Ref 53). Double-burst conditions (fireball and shock wave interaction, and torus formation) have been studied (Ref 149), as have also the dynamics of dust formation and motion (Refs 25,26 117). Performance tests were run on a naval blast valve (Ref 92), and on aircraft wing panels (Ref 4)... 

In this section, inert or nonreactive shock waves are discussed. We will learn the behavior of shocks by studying simple, mechanically analogous models and then proceed to develop the basic equations that describe dynamic uniaxial strain (shocks in only one direction). We will see how these equations are supplemented by experimentally derived empirical correlations, which will then allow us to solve them for simple shock wave interactions. 

The pressure at the interface of the charge and the water can be found by solving the shock wave interaction between the explosive detonation products P-u isentrope and the P-u Hugoniot for water (for TNT this is around 120 kbar). This point (at RIRq = 1) can then be extrapolated back to the Eq. (28.3) curve of P = f(RIRo) using a power fit (a straight line on a log-log plot). This line should come tangent to the P versus R/Rq curve. This is shown in Figure 28.7 for Pvs R/Ro for TNT under water. 

Section 111 deals with nonreactive shock waves. The thread here is composed of three simple equations that describe the conservation of mass, momentum, and energy across the shock front. In this section we learn how to deal quantitatively with shock waves interacting with material interfaces and other shock waves. 

I hc-sc results deinou.slrale llutl the molar yield in shock reaction is controlled by the. shock period, and that the shock reaction proceeds only during the period in which the shock wave interacts witli hexane. 

Polachek, H., and Seeger, R.J., Shock Wave Interactions, Fundamentals of Gas Dynamics Vol. Ill of High Speed Aerodynamics and Jet Propulsion, edited by H.W. Emmons, Princeton Univ. Press, Princeton, NJ, 1958. 

Glowacki, W.J., Kuhl, A.L., Glaz, H.M., and Ferguson, R.E., Shock Wave Interaction with High Sound Speed Layers, Proceedings of the 15th International Symposium on Shock Waves and Shock Tubes, edited by D. Bershader and R. Hanson, Stanford Univ. Press, Palo Alto, CA, 1986. 

A shock wave Interacting with a liquid-air interface is able to generate cavitation and small bubbles, the implosion of which are responsible for micro jets and the production of small droplets in air. New studies of the implosion of the bubbles are needed to contribute to the behavior of cavitated liquid supporting chemical reactions. 

The hot spot formed when a shock wave interacts with a spherical hole scales with the radius of the hole as long as no chemical reaction occurs. Using hot spot temperatures in the calculated range of 700 to 1300°K and calculating the adiabatic explosion is shown below. The ordering is identical to that observed experimentally. 

The experimental run to detonation values are about the same for a 125 kbar shock wave interacting with TATB with 10% voids, for a 50 kbar shock wave interacting with HMX with 10% voids, and for a 20 kbar shock wave interacting with PETN with 10% voids. 

To investigate the effect of the interaction of a matrix of holes with a multiple shock profile, a matrix of 10% air holes located on a hexagonal close-packed lattice in TATB was modeled. The spherical air holes had a diameter of 0.004 cm. The initial configuration is shown in Figure 3.39. The three-dimensional computational grid contained 16 by 22 by 36 cells each 0.001 cm on a side. The time step was 0.0002 /rsec. Figure 3.40 shows the density and mass fraction cross sections for a 40 kbar shock wave followed after 0.045 /rsec by a 290 kbar shock wave interacting with a matrix of 10% air holes of 0.004 cm diameter in TATB. 

The three-dimensional modeling study demonstrated that the desensitization occurs because the preshock interacts with the holes and eliminates the density discontinuities. The subsequent higher pressure shock waves interact with a more homogeneous explosive. The multiple shock temperature is lower than the single shock temperature at the same pressure, which is the cause of the observed failure of a detonation wave to propagate in preshocked explosive for some ranges of preshock pressure. 

Figure 3.40 The density and mass fraction cross sections are shown for a 40 kbar shock wave, followed after 0.045 jisec by a 290 kbar shock wave interacting with a matrix of 10% holes of 0.004 cm diameter in TATB.

Since the initiators for insensitive high explosives must be very large to initiate propagating detonation, other methods have been studied to achieve the required high pressures of adequate duration. High pressures are achieved if two or more shock waves interact to form regular or Mach shock interactions. 

The use of multiple shock wave interactions to initiate propagating detonation has been studied experimentally by Goforth . He observed that while double shock wave interactions were sometimes inadequate to initiate propagating detonation, triple shock wave interactions could be generated that initiated propagating detonation in insensitive high explosives. 

Based on the general experience of studying gas-dynamics of combustible/ noncombustible mixtures, it seems convenient to perform an investigation of shock (blast) wave focusing at their interaction with concave reflecting surfaces. By now, a sufficient experimental-theoretical database has been collected to allow description of the shock wave interaction with two-dimensional and three-dimensional concave reflectors in noncombustible gases. 

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